Ok so, Henry VII is left with a girl, who I shall call Margaret for simplicities sake. Little Margaret was born in 1501, as was described the OP. Margaret Tudor I of England is married to he uncle and co-monarch shortly after her ascension. The marriage can't be consummated until a leas 1513, though I don't see children until around 1516/1517. Judging by Henry's track record OTL and her maternal ancestry, I can see about 6/7 pregnancies and maybe 1/2 living children.
During this time, Catherine most likely beats off the suitors, with the most consistent for a time being either Charles Brandon or Thomas Howard. If she does remarry, it'll be to gain influence at the court and protect her daughter, so I see maybe Thomas Grey, 2nd Marquess of Dorset as a good option. If this happens, her father will not be happy but I an see her doing something like this to protect her daughter. Another option is that she's married off somewhere else, maybe to Charles III, Duke of Savoy.
So, basically:
1501: Margaret Tudor of Wales is born.
1502: Arthur, Prince of Wales dies.
1507: The dispension to marry Henry, Duke of York to his niece Margaret Tudor secretly arrives in England.
1509: Henry VII of England dies. Margaret I of England ascends and is married to her uncle, Henry Tudor, Duke of York, who becomes Henry VIII of England alongside his child bride.
1510: Fearing her lack of influence at court and wanting to act as a protector of her daughter, a position taken over by her brother-in-law, Catherine of Aragon marries Thomas Grey, 2nd Marquess of Dorset.
1511: Catherine of Aragon gives birth to her second child, Henry Grey.
1512: Catherine of Aragon gives birth to her third child, Elizabeth Grey.
1513: Catherine of Aragon gives birth to her fourth child, Thomas Grey. Elizabeth Grey dies.
1514: Henry VIII and Margaret I of England consummate their union. Catherine of Aragon gives birth to her fifth child: Mary Grey.
1516: Margaret I of England gives birth to her first child, a stillborn boy.
1517: Catherine of Aragon gives birth to her sixth child, John Grey. He dies a few days after birth.
1519: Margaret I of England gives birth to her second child, Elizabeth Tudor.
1520: Margaret I of England gives birth to her third child, Henry Tudor. He dies a month later.
1522: Margaret I of England gives birth to her fourth child, Edward Tudor.
1523: Margaret I of England gives birth to her fifth child, a stillborn boy.
1526: Margaret I of England gives birth to her sixth child, Mary Tudor. The child dies a week after birth.
1530: Thomas Grey, 2nd Marquess of Dorset dies, leaving Catherine of Aragon a widow for the second time.
1531: Margaret I of England gives birth to her seventh child, Catherine Tudor.
1536: Catherine of Aragon dies.
1538: Henry VIII of England dies in a hunting accident, though many will say his wife had him killed after he threatened to put her in a nunnery an take a young, pretty wife.
1543: Margaret I of England dies and her son Edward VI of England takes the throne.
Catherine of Aragon (b.1485: d.1536) m. Arthur, Prince of Wales (b.1486: d.1502) (a), Thomas Grey, 2nd Marquess of Dorset (b.1477: d.1530) (b)
1a) Margaret I of England (b.1501) m. Henry VIII of England (b.1491: d.1538) (a)
1a) Stillborn Boy (c.1516)
2a) Elizabeth Tudor (b.1519)
3a) Henry Tudor (b.1520: d.1520)
4a) Edward VI of England (b.1522)
5a) Stillborn Boy (c.1523)
6a) Mary Tudor (b.1526: d.1526)
7a) Catherine Tudor (b.1531)
2b) Henry Grey, Marquess of Dorset (b.1511) m. m. Margaret Douglas (b.1515: d.1578) (a)
1a) Elizabeth Grey (b.1543)
2a) Henry Grey (b.1548)
3a) Stillborn Boy (c.1550)
4a) Edward Grey (b.1552: d.1560)
3b) Elizabeth Grey (b.1512: d.1513)
4b) Sir Thomas Grey (b.1513) m. Mary Brandon (b.1510: d.1544) (a)
1a) Penelope Grey (b.1525)
2a) Marian Grey (b.1527: d.1528)
3a) Anne Grey (b.1529: d.1532)
4a) Charles Grey (b.1530)
5a) Stillborn Boy (c.1533)
5b) Mary Grey (b.1514: d.1544) m. Thomas Stanley, 2nd Baron Monteagle (c.1510: d.1550) (a)
1a) Stillborn Boy (c.1534)
2a) Francis Stanley, 3rd Baron Monteagle (b.1535: d.1554)
3a) William Stanley, 4th Baron Monteagle (b.1536: d.1559)
4a) Anne Stanley (b.1538)
5a) Thomas Stanley, 5th Baron Monteagle (b.1541)
6a) Miscarriage (c.1542)
7a) Stillborn Girl (c.1544)
8a) Henry Stanley (b.1545: d.1545)
6a) John Grey (b.1517: d.1517)