But her experiences raise questions about whether all players are receiving sufficient level of support when it comes to maternity leave.
Brynjarsdóttir announced in August that she would miss most of the 2023/24 season as she prepared to give birth to her second child.
She told talkSPORT how dealing with her pregnancy and trying to maintain her training schedule with West Ham had been a balancing act.
She said: "I'm not going to lie, I'm not great at being pregnant!
"It's just hard as an athlete when you're used to being fit, controlling your body and then all of a sudden you don't.
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"I'm still pregnancy sick, even though I'm in the third trimester. Still throwing up most days, so it's a bit of a struggle.
"But I know it's just temporary, and I will get a great reward in the end so it's all going to be worth it."
When asked how vital it was that West Ham were supporting her throughout her pregnancy, Brynjarsdóttir said flexibility from her club was key.
She said: "Obviously, when you're pregnant as a football player, you have a different role on the team and just the hormones, everything, there's a lot of feelings, emotions going around.
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"It's just very important that the club supports you - and supports you in every way.
"I try to come in every day - but still, there are days where I'm too sick to come in. And they're ok with it.
"They support my training sessions, I get treatment. Just feeling the support through the pregnancy and knowing that they're going to be there for you after giving birth, I think that's a big thing."
And while the West Ham captain might not be with her team on the pitch, she is still spending as much time around the squad as she possible can.
She said: "I'm in training with them almost every day when they're in.
"I don't go to the away games now. but I go to every home game - I've only missed one this season because I was too sick to go, so I had to watch it on TV!"
She added: "I'm their biggest fan this season!"
Under the current WSL policy, players going on maternity leave are entitled to 14 weeks on their regular salary.
By comparison, the UK government's national policy entitles women to up to 52 weeks of Statutory Maternity Leave - more than three times that of the WSL policy.
But even the 14-week policy is a relatively recent development in the women's game.
It was only in September 2022 that former Lioness and Everton winger Toni Duggan became the first WSL player to receive official maternity payments.
Previously, maternity payments had been the decision of individual clubs and the legislation that changed that was only introduced at the start of the 2022/23 season.
Clubs still have the option to extend the 14-week period if they feel players require extra support.
In January 2023, former Reading defender and Scottish international Emma Mukandi expressed concern about the inadequacy of the existing policy after she described her own difficult maternity period.
Mukandi told Off The Ball's COYGIG podcast: "The policy is you only get 14 weeks' full pay and then you've got to go back to your work.
"Bear in mind our body is our job, who even came up with that? Surely not someone who's played football and had a baby.
"Is that a man? It had to be a man. A man was definitely involved in that."
Mukandi added that financial discrepancies between clubs meant a universal maternity policy was bound to make things more difficult for those in lower-tier sides.
She said: "I had to fake an injury because I didn't want to tell anyone I was pregnant until the ten-week scan.
"It comes down to whatever club you're at. If you've got loads of money at Arsenal, Chelsea and Manchester City, you've got loads of great facilities, having a baby there is not an issue at all.
"But the lower down the leagues you go and then money comes into it and facilities, then it's easier for clubs and CEOs to be like, 'No, this isn't happening'."
Clubs like Chelsea have been seen to offer high levels of support to players who need to take maternity leave.
Chelsea midfielder Melanie Leupolz recently become one of a growing number of WSL players to have a child and return to play in a short space of time.
After giving birth in October 2022, Leupolz returned to the pitch less than four months later in January 2023.
And manager Emma Hayes went to great lengths to make sure Leupolz had as much support as possible.
Leupolz told Sky Sports in March 2023: "Emma has a child herself and she knows what's important.
"She said to our physios that they had to implement a pelvic floor specialist. I can work with her and after pregnancy, I can see if I'm back where I was before.
"To be honest, that was a game changer, it was really important."
Mukandi, on the other hand, said Reading - who were relegated from the WSL last season - had not allowed her to bring her daughter to the training ground when she could not arrange childcare due to a club policy.
For players, the process of returning to play after giving birth is thus often dependent on their club.
Brynjarsdóttir returned to training with Portland Thorns, where she played from 2016 to 2019, less than a week after giving birth to her first child - but she admitted that process was always subject to the smoothness of the pregnancy.
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She said: "I don't want to put my goals too high because after pregnancy you never know how it's going to go.
"But I know I will work hard to get back to myself and try to be a better player than I was before."